R13 understand that X is inversely proportional to Y is equivalent to X is proportional to Quiz: Pearson Edexcel Maths, Unit 3

The 20 questions

1. If X is inversely proportional to Y, then X is proportional to:

   • 1/Y
   • Y²
   • 1/Y²
   • Y

2. Which equation expresses X inversely proportional to Y with constant k?

   • X = k/Y
   • X = k/Y²
   • X = Y/k
   • X = kY

3. Which algebraic expression means y is inversely proportional to x squared?

   • y equals k over x squared
   • y equals k over x
   • y equals x squared over k
   • y equals k x squared

4. To find the constant k in X = k/Y, you calculate:

   • X added to Y
   • X multiplied by Y
   • X divided by Y
   • Y subtracted from X

5. What shape is the graph of X against Y when X is inversely proportional to Y?

   • Rectangular hyperbola
   • Cubic curve
   • Parabola
   • Straight line

6. If X is directly proportional to Z and inversely proportional to Y, which equation holds?

   • X = kZY
   • X = kY/Z
   • X = kZ/Y
   • X = k/(ZY)

7. If X is inversely proportional to Y³, then X is proportional to:

   • 1/(3Y)
   • 3Y
   • Y³
   • 1/Y³

8. For X inversely proportional to Y, what remains constant?

   • the ratio X/Y
   • the product XY
   • the difference X − Y
   • the sum X + Y

9. X is inversely proportional to Y. X = 6 when Y = 5. What is X when Y = 2?

   • 2.4
   • 12
   • 6
   • 15

10. Y varies inversely as the square of X. Y = 4 when X = 3. What is Y when X = 6?

    • 8
    • 1
    • 0.5
    • 2

11. X is proportional to 1/Y. X = 0.4 when Y = 15. What is Y when X = 3?

    • 22.5
    • 0.2
    • 2
    • 45

12. The time to paint a room varies inversely with the number of painters. 4 painters take 6 hours. How long do 8 painters take?

    • 3 hours
    • 12 hours
    • 24 hours
    • 1.5 hours

13. Given X = 12/Y, what is Y when X = 3?

    • 36
    • 0.25
    • 9
    • 4

14. If X equals 50 over Y and Y doubles, what happens to X?

    • It halves
    • It stays same
    • It doubles
    • It quarters

15. Which equation models X inversely proportional to the square root of Y?

    • X = k√Y
    • X = k/Y
    • X = kY/√Y
    • X = k/√Y

16. p is directly proportional to q and inversely proportional to r². p = 2 when q = 8 and r = 4. Find p when q = 3 and r = 2.

    • 12
    • 0.75
    • 6
    • 3

17. If Y varies inversely with the square of Z, what happens to Y when Z doubles?

    • Halved
    • Doubled
    • Divided by four
    • Multiplied by four

18. What is a key feature of the graph of X equals 12 over Y for positive values?

    • Asymptotic to axes
    • Vertical line
    • Crosses origin
    • Horizontal line

19. If X is inversely proportional to Y and Y is inversely proportional to Z, how does X relate to Z?

    • Unrelated
    • Directly proportional
    • Constant
    • Inversely proportional

20. X is inversely proportional to Y. X = 3 when Y = 12. What is X when Y = 9?

    • 12
    • 3
    • 2.25
    • 4

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